Compute an approximated sample size for linear mixed models (two-level-designs), based on power-calculation for standard design and adjusted for design effect for 2-level-designs.

```
samplesize_mixed(
eff.size,
df.n = NULL,
power = 0.8,
sig.level = 0.05,
k,
n,
icc = 0.05
)
smpsize_lmm(
eff.size,
df.n = NULL,
power = 0.8,
sig.level = 0.05,
k,
n,
icc = 0.05
)
```

eff.size | Effect size. |
---|---|

df.n | Optional argument for the degrees of freedom for numerator. See 'Details'. |

power | Power of test (1 minus Type II error probability). |

sig.level | Significance level (Type I error probability). |

k | Number of cluster groups (level-2-unit) in multilevel-design. |

n | Optional, number of observations per cluster groups (level-2-unit) in multilevel-design. |

icc | Expected intraclass correlation coefficient for multilevel-model. |

A list with two values: The number of subjects per cluster, and the total sample size for the linear mixed model.

The sample size calculation is based on a power-calculation for the
standard design. If `df.n`

is not specified, a power-calculation
for an unpaired two-sample t-test will be computed (using
`pwr.t.test`

of the pwr-package).
If `df.n`

is given, a power-calculation for general linear models
will be computed (using `pwr.f2.test`

of the
pwr-package). The sample size of the standard design
is then adjusted for the design effect of two-level-designs (see
`design_effect`

). Thus, the sample size calculation is appropriate
in particular for two-level-designs (see Snijders 2005). Models that
additionally include repeated measures (three-level-designs) may work
as well, however, the computed sample size may be less accurate.

Cohen J. 1988. Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale,NJ: Lawrence Erlbaum.

Hsieh FY, Lavori PW, Cohen HJ, Feussner JR. 2003. An Overview of Variance Inflation Factors for Sample-Size Calculation. Evaluation and the Health Professions 26: 239-257. doi: 10.1177/0163278703255230

Snijders TAB. 2005. Power and Sample Size in Multilevel Linear Models. In: Everitt BS, Howell DC (Hrsg.). Encyclopedia of Statistics in Behavioral Science. Chichester, UK: John Wiley and Sons, Ltd. doi: 10.1002/0470013192.bsa492

```
# Sample size for multilevel model with 30 cluster groups and a small to
# medium effect size (Cohen's d) of 0.3. 27 subjects per cluster and
# hence a total sample size of about 802 observations is needed.
samplesize_mixed(eff.size = .3, k = 30)
#> $`Subjects per Cluster`
#> [1] 27
#>
#> $`Total Sample Size`
#> [1] 802
#>
# Sample size for multilevel model with 20 cluster groups and a medium
# to large effect size for linear models of 0.2. Five subjects per cluster and
# hence a total sample size of about 107 observations is needed.
samplesize_mixed(eff.size = .2, df.n = 5, k = 20, power = .9)
#> $`Subjects per Cluster`
#> [1] 5
#>
#> $`Total Sample Size`
#> [1] 107
#>
```